Electrical conduction at the single molecule scale has been studied extensively with molecular nanojunctions. Measurements have revealed a wealth of interesting physics. I3owever; our understanding is hindered by a lack of methods for simultaneous local imaging or spectroscopy to determine the conformation and local environment of the molecule of interest. Optical molecular spectroscopies have made significant progress in recent years, with single molecule sensitivity achieved through the use of surface-enhanced spectroscopies. In particular surface-enhanced Raman spectroscopy (SERS) has been demonstrated to have single molecule sensitivity for specific plasmonic structures. Many unanswered quest ions remain about the SERS process, particularly the role of chemical enhancements of the Raman signal. The primary goal of the research presented here is to combine both electrical and optical characterization techniques to obtain a more complete picture of electrical conduction at the single or few molecule level. We have successfully demonstrated that nanojunctions are excellent SERS substrates with the ability to achieve single molecule sensitivity. This is a major accomplishment with practical applications in optical sensor design. We present a method for mass producing nanojunctions with SERS sensitivity optimized through computer modeling. We have demonstrated simultaneous optical and electrical measurements of molecular junctions with single molecule electrical and SERS sensitivity. Measurements show strong correlations between electrical conductance and changes to the SERS response of nanojunctions. These results allow for one of the most conclusive demonstrations of single molecule SERS to date. This measurement technique provides the framework for three additional studies discussed here as well as opening up the possibilities for numerous other experiments. One measurement examines heating in nanowires rather than nanojunctions. We observe that, the electromigration process used to turn Pt nanowires into nanojunctions heats the wires to temperatures in excess of 1000 K, indicating that thermal decomposition of molecules on the nanowire is a major problem. Another measurement studies optically driven currents in nanojunctions. The photocurrent is a result of rectification of the enhanced optical electric field in the nanogap. From low frequency electrical measurements we are able to infer the magnitude of the enhanced electric field, with inferred enhancements exceeding 1000. This work is significant to the field of plasmonics and shows the need for more complete quantum treatments of plasmonic structures. Finally we investigate electrical and optical heating in molecular nanojunctions. Our measurements show that molecular vibrations and conduction electrons in nano-junctions under electrical bias or laser illumination can be driven from equilibrium to temperatures greater than 600 K. We observe that individual vibrations are also not in thermal equilibrium with one another. Significant heating in the conduction electrons in the metal electrodes was observed which is not expected in the ballistic tunneling model for electrons in nanojunctions this indicates a need for a more completely energy dissipation theory for nanojunctions.

High angular momentum Rydberg wave packets are studied. Application of carefully tailored electric fields to low angular momentum, high- n ( n ∼ 300) Rydberg atoms creates coherent superpositions of Stark states with near extreme values of angular momentum, [cursive l]. Wave packet components orbit the parent nucleus at rates that depend on their energy, leading to periods of localization and delocalization as the components come into and go out of phase with each other. Monitoring survival probability signals in the presence of position dependent probing leads to observation of characteristic oscillations based on the composition of the wave packet. The discrete nature of electron energy levels is observed through the measurement of quantum revivals in the wave packet localization signal. Time-domain spectroscopy of these signals allows determination of both the population and phase of individual superposition components. Precise manipulation of wave packets is achieved through further application of pulsed electric fields. Decoherence effects due to background gas collisions and electrical noise are also detailed. Quantized classical trajectory Monte-Carlo simulations are introduced and agree remarkably well with experimental results.

Silicon oxide (SiO x 1 ∠ x [∠, double =]2) has long been used and considered as a passive and insulating component in the construction of electronic devices. In contrast, here the active role of SiO x in constructing a type of resistive switching memory is studied. From electrode-independent electrical behaviors to the visualization of the conducting filament inside the SiO x matrix, the intrinsic switching picture in SiO x is gradually revealed. The thesis starts with the introduction of some similar phenomenological switching behaviors in different electronic structures (Chapter 1), and then generalizes the electrode-material-independent electrical behaviors on SiO x substrates, providing indirect evidence to the intrinsic SiO x switching (Chapter 2). From planar nanogap systems to vertical sandwiched structures, Chapter 3 further discusses the switching behaviors and properties in SiO x . By localization of the switching site, the conducting filament in SiO x is visualized under transmission electron microscope using both static and in situ imaging methods (Chapter 4). With the intrinsic conduction and switching in SiO x largely revealed, Chapter 5 discusses its impact and implications to the molecular electronics and nanoelectronics where SiO x is constantly used. As comparison, another type of memory effect in semiconductors (carbon nanotubes) based on charge trapping at the semiconductor/SiO x interface is discussed (Chapter 6).

This work aims to improve the capability of accurate information extraction from high-dimensional data, with a specific neural learning paradigm, the Self-Organizing Map (SOM). The SOM is an unsupervised learning algorithm that can faithfully sense the manifold structure and support supervised learning of relevant information from the data. Yet open problems regarding SOM learning exist. We focus on the following two issues. (1) Evaluation of topology preservation. Topology preservation is essential for SOMs in faithful representation of manifold structure. However, in reality, topology violations are not unusual, especially when the data have complicated structure. Measures capable of accurately quantifying and informatively expressing topology violations are lacking. One contribution of this work is a new measure, the Weighted Differential Topographic Function ( WDTF ), which differentiates an existing measure, the Topographic Function ( TF ), and incorporates detailed data distribution as an importance weighting of violations to distinguish severe violations from insignificant ones. Another contribution is an interactive visual tool, TopoView, which facilitates the visual inspection of violations on the SOM lattice. We show the effectiveness of the combined use of the WDTF and TopoView through a simple two-dimensional data set and two hyperspectral images. (2) Learning multiple latent variables from high-dimensional data. We use an existing two-layer SOM-hybrid supervised architecture, which captures the manifold structure in its SOM hidden layer, and then, uses its output layer to perform the supervised learning of latent variables. In the customary way, the output layer only uses the strongest output of the SOM neurons. This severely limits the learning capability. We allow multiple, k , strongest responses of the SOM neurons for the supervised learning. Moreover, the fact that different latent variables can be best learned with different values of k motivates a new neural architecture, the Conjoined Twins, which extends the existing architecture with additional copies of the output layer, for preferential use of different values of k in the learning of different latent variables. We also automate the customization of k for different variables with the statistics derived from the SOM. The Conjoined Twins shows its effectiveness in the inference of two physical parameters from Near-Infrared spectra of planetary ices.

The electronic structure and optical properties of metallic nanoparticles are theoretically investigated front first principles. An efficient implementation of time-dependent density functional theory allows a fully quantum mechanical description of systems large enough to display collective electron oscillations and surface plasmon modes. The results are compared with traditional classical electrodynamical approaches. Different regimes of interest are identified, both where classical electrodynamical models yield accurate descriptions, and where quantum effects are indispensable for understanding plasmonic properties in nanostructures. The limits of validity of classical electrodynamics are clearly established for the study of a variety of relevant geometries.

This thesis develops models for accurate prediction of price changes on electronic stock exchanges by utilizing autoregressive and logistic methods. Prices on these electronic stock exchanges, also called ECNs, are solely determined by where orders have been placed into the order book, unlike traditional stock exchanges where prices are determined by an expert market maker. Identifying the significant variables and formulating the models will provide critical insight into the dynamics of prices on ECNs. Whereas previous research has relied on simulated data to test market strategies, this analysis will utilize actual ECN data. The models recognize patterns of asymmetry and movement of the shares in the order book to formulate accurate probabilities for possible future price changes. On traditional stock exchanges, price changes could only occur as quickly as human beings could enact them. On ECNs, computerized systems place orders on behalf of traders based on their preferences, resulting in price changes that reflect trader activity almost instantaneously. The quickness of this automation on ECNs forces the re-evaluation of commonly held beliefs about stock price dynamics. Previous strategies developed for trading on ECNs have relied mainly on price fluctuations to gain profits. This thesis uses the formulated models to design profitable strategies that use accurate prediction rather than price variability.

This thesis details the development of ultra-short, single-walled carbon nanotubes (US-tubes) for use as nanocapsules to contain and deliver medical agents for both imaging (Gd3+ ) and therapeutic (211 At) purposes. In particular, Gd3+ -loaded US-tubes, known as gadonanotubes, operate as high-performance MRI contrast agents with relaxivities (image enhancement efficacy) a factor of 40-100 greater than current clinical contrast agents. Furthermore, gadonanotube relaxivities are highly pH-dependent, with image intensity nearly tripling from pH 7.5 to 6.8. Coupled with their high efficacies and targeting potential, these agents are promising candidates for next-generation targeted imaging probes for the early detection of cancer. Single gadonanotubes have also been encapsulated in a polymer shell for use as an intravenous MRI contrast agent. In addition, a new functionalization scheme has been developed to covalently attach a variety of amino acids in high quantity to the outer surface of the gadonanotubes and to attach a small peptide sequence for targeting breast cancer cells. The gadonanotubes have also been used as magnetic cell labeling agents, while also demonstrating efficacy in vivo as contrast agents. In addition to functioning as an imaging agent platform, the US-tubes have demonstrated efficacy as nanocapsules for radiotherapeutic agents. Astatine-211 (At-211), an α-emitting radionuclide, can be loaded inside the US-tube with excellent containment stability for the targeted delivery of an α-radiotherapeutic agent to micrometastatic and single-cell cancers. The loading levels for At-211 are comparable to, or better than, other known compounds. At-211, existing as the mixed-halogen compound 211 AtCl, is retained in the US-tube nanocapsules due to van der Waals forces between the 211AtCl and the interior sidewalls of the nanotube. Finally, the US-tubes have been shown to induce few health risks in mammalian experiments. Acute toxicity tests were conducted on mice with both raw and purified full-length carbon nanotubes (SWNTs), as well as US-tubes, using large doses (up to 1 g/kg of bodyweight). Even at these large doses, no animal death was recorded, although in a few cases behavioral changes were observed. Nanotubes were observed to be eliminated from the liver and kidneys through the urine and feces. It is believed that any toxicity at high doses can be attenuated (and prevented) by properly formulating the administered dose.

By treating free electrons in metallic nanostructures as incompressible and irrotational fluid, Plasmon hybridization (PH) method can be used as a very useful tool in interpolating the electric magnetic behaviors of complex metallic nanostructures. Using PH theory and Finite Element Method (FENI), we theoretically investigated the optical properties of some complex nanostructrus including coupled nanoparticle aggregates and nanowires. We investigated the plasmonic properties of a symmetric silver sphere heptamer and showed that the extinction spectrum exhibited a narrow Fano resonance. Using the plasmon hybridization approach and group theory we showed that this Fano resonance is caused by the interference of two bonding dipolar subradiant and superradiant plasmon modes of E1u symmetry. We investigate the effect of structural symmetry breaking and show that the energy and shape of the Fano resonance can be tuned over a broad wavelength range. We show that the wavelength of the Fano resonance depends very sensitively on the dielectric permittivity of the surrounding media. Besides heptamer, we also used plasmon hybridization method and finite element method to investigate the plasmonic properties of silver or gold nano spherical clusters. For symmetric clusters, we show how group theory can be used to identify the microscopic nature of the plasmon resonances. For larger clusters, we show that narrow Fano resonances are frequently present in their optical spectra. As an example of asymmetric clusters, we demonstrate that clusters of four identical spherical particles support strong Fano-like interference. This feature is highly sensitive to the polarization of the incident electric field due to orientation-dependent coupling between particles in the cluster. Nanowire plasmons can be launched by illumination at one terminus of the nanowire and emission can be detected at the other end of the wire. With PH theory we can predict how the polarization of the emitted light depends on the polarization of the incident light. Depending on termination shape, a nanowire can serve as either a polarization-maintaining waveguide, or as a polarization-rotating, nanoscale half-wave plate. We also investigated how the properties of a nearby substrate modify the excitation and propagation of plasmons in subwavelength silver wires.

The usual approach to the study of signaling pathways in biological systems is to assume that high numbers of cells and of perfectly mixed molecules within cells are involved. To study the temporal evolution of the system averaged over the cell population, ordinary differential equations are usually used. However, this approach has been shown to be inadequate if few copies of molecules and/or cells are present. In such situation, a stochastic or a hybrid stochastic/deterministic approach needs to be used. Moreover, considering a perfectly mixed system in cases where spatial effects are present can be an over-simplifying assumption. This can be corrected by adding diffusion terms to the ordinary differential equations describing chemical reactions and proliferation kinetics. However, there exist cases in which both stochastic and spatial effects have to be considered. We study the relevance of differential equations, stochastic Gillespie algorithm, and deterministic and stochastic reaction-diffusion models for the study of important biological processes, such as viral infection and early carcinogenesis. To that end we have developed two optimized libraries of C functions for R (r-project.org) to simulate biological systems using Petri Nets, in a pure deterministic, pure stochastic, or hybrid deterministic/stochastic fashion, with and without spatial effects. We discuss our findings in the terms of specific biological systems including signaling in innate immune response, early carcinogenesis and spatial spread of viral infection.

This thesis presents a robust solution to the classification and variable selection problem when the dimension of the data, or number of predictor variables, may greatly exceed the number of observations. When faced with the problem of classifying objects given many measured attributes of the objects, the goal is to build a model that makes the most accurate predictions using only the most meaningful subset of the available measurements. The introduction of [cursive l] 1 regularized model titling has inspired many approaches that simultaneously do model fitting and variable selection. If parametric models are employed, the standard approach is some form of regularized maximum likelihood estimation. While this is an asymptotically efficient procedure under very general conditions, it is not robust. Outliers can negatively impact both estimation and variable selection. Moreover, outliers can be very difficult to identify as the number of predictor variables becomes large. Minimizing the integrated squared error, or L 2 error, while less efficient, has been shown to generate parametric estimators that are robust to a fair amount of contamination in several contexts. In this thesis, we present a novel robust parametric regression model for the binary classification problem based on L 2 distance, the logistic L 2 estimator (L 2 E). To perform simultaneous model fitting and variable selection among correlated predictors in the high dimensional setting, an elastic net penalty is introduced. A fast computational algorithm for minimizing the elastic net penalized logistic L 2 E loss is derived and results on the algorithm's global convergence properties are given. Through simulations we demonstrate the utility of the penalized logistic L 2 E at robustly recovering sparse models from high dimensional data in the presence of outliers and inliers. Results on real genomic data are also presented.